Rat Locomotion Analysis Based on Straight Line Detection in Hough Space
This paper demonstrates a method to perform movement analysis on rats named Movement Measurement in Hough Transform Space (MMHTS). The MMHTS method consists of representing locomotion of movement based on a system of linear equations and subsequently detecting the straight lines in the Hough transfo...
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2025-07-01
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| author | José Trinidad Guillen Bonilla Héctor Guillen Bonilla Nancy Elizabeth Franco Rodríguez Mario Alberto García Ramírez Alex Guillen Bonilla Maricela Jiménez Rodríguez María Eugenia Sánchez Morales |
| author_facet | José Trinidad Guillen Bonilla Héctor Guillen Bonilla Nancy Elizabeth Franco Rodríguez Mario Alberto García Ramírez Alex Guillen Bonilla Maricela Jiménez Rodríguez María Eugenia Sánchez Morales |
| author_sort | José Trinidad Guillen Bonilla |
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| description | This paper demonstrates a method to perform movement analysis on rats named Movement Measurement in Hough Transform Space (MMHTS). The MMHTS method consists of representing locomotion of movement based on a system of linear equations and subsequently detecting the straight lines in the Hough transform space. Four straight lines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> are detected, and with their information the angles between the beelines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula>, intersection points <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula> and their lengths <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula> are measured, corresponding to the locomotion geometry of the rats’ limps. Experimentally, the MMHTS method was employed for locomotion movement and the obtained results were compared with professional design software, detecting the following miscalculations: 0.144° for the angle measurements, 0.131 for the length measurement and 0.139 for the point detection. Based in the measurements results and the calculated errors, the MMHTS method is efficient and exhibits a high application potential in motion analysis. |
| format | Article |
| id | doaj-art-9ad3b5609cba49239c97e7f0ebbda497 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-9ad3b5609cba49239c97e7f0ebbda4972025-08-20T02:36:26ZengMDPI AGMathematics2227-73902025-07-011313218710.3390/math13132187Rat Locomotion Analysis Based on Straight Line Detection in Hough SpaceJosé Trinidad Guillen Bonilla0Héctor Guillen Bonilla1Nancy Elizabeth Franco Rodríguez2Mario Alberto García Ramírez3Alex Guillen Bonilla4Maricela Jiménez Rodríguez5María Eugenia Sánchez Morales6Departamento de Electro-Fotónica, Centro Universitario de Ciencias Exactas e Ingenierías, Blvd. Gral. Marcelino García Barragán 1421, Guadalajara 44430, Jalisco, MexicoDepartamento de Ingeniería de Proyectos, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Blvd M. García Barragán 1421, Guadalajara 44430, Jalisco, MexicoDepartamento de Farmacobiología, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Blvd M. García Barragán 1421, Guadalajara 44430, Jalisco, MexicoDepartamento de Electro-Fotónica, Centro Universitario de Ciencias Exactas e Ingenierías, Blvd. Gral. Marcelino García Barragán 1421, Guadalajara 44430, Jalisco, MexicoDepartamento de Ciencias Computacionales e Ingeniería, Centro Universitario de los Valles, Universidad de Guadalajara, Carretera Guadalajara-Ameca Km. 45.5, Ameca 46600, Jalisco, MexicoDepartamento de Ciencias Básicas, Centro Universitario de la Ciénega, Universidad de Guadalajara, Av. Universidad No. 1115, LindaVista, Ocotlán 47810, Jalisco, MexicoDepartamento de Ciencias Tecnológicas, Centro Universitario de la Ciénega, Universidad de Guadalajara, Av. Universidad No. 1115, Lindavista, Ocotlán 47810, Jalisco, MexicoThis paper demonstrates a method to perform movement analysis on rats named Movement Measurement in Hough Transform Space (MMHTS). The MMHTS method consists of representing locomotion of movement based on a system of linear equations and subsequently detecting the straight lines in the Hough transform space. Four straight lines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> are detected, and with their information the angles between the beelines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula>, intersection points <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula> and their lengths <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula> are measured, corresponding to the locomotion geometry of the rats’ limps. Experimentally, the MMHTS method was employed for locomotion movement and the obtained results were compared with professional design software, detecting the following miscalculations: 0.144° for the angle measurements, 0.131 for the length measurement and 0.139 for the point detection. Based in the measurements results and the calculated errors, the MMHTS method is efficient and exhibits a high application potential in motion analysis.https://www.mdpi.com/2227-7390/13/13/2187motion analysisimage processingmovement measurement on hough transform space (MMHTS) methodhough transformstraight line detectionhigh application potential in motion analysis |
| spellingShingle | José Trinidad Guillen Bonilla Héctor Guillen Bonilla Nancy Elizabeth Franco Rodríguez Mario Alberto García Ramírez Alex Guillen Bonilla Maricela Jiménez Rodríguez María Eugenia Sánchez Morales Rat Locomotion Analysis Based on Straight Line Detection in Hough Space Mathematics motion analysis image processing movement measurement on hough transform space (MMHTS) method hough transform straight line detection high application potential in motion analysis |
| title | Rat Locomotion Analysis Based on Straight Line Detection in Hough Space |
| title_full | Rat Locomotion Analysis Based on Straight Line Detection in Hough Space |
| title_fullStr | Rat Locomotion Analysis Based on Straight Line Detection in Hough Space |
| title_full_unstemmed | Rat Locomotion Analysis Based on Straight Line Detection in Hough Space |
| title_short | Rat Locomotion Analysis Based on Straight Line Detection in Hough Space |
| title_sort | rat locomotion analysis based on straight line detection in hough space |
| topic | motion analysis image processing movement measurement on hough transform space (MMHTS) method hough transform straight line detection high application potential in motion analysis |
| url | https://www.mdpi.com/2227-7390/13/13/2187 |
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